## Linear Operators: Spectral theory |

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Page 884

The study of ideal theory in B-algebra was inaugurated by Gelfand [1] to whom

most of the results

Section 2 are due to Gelfand [1]. The fundamental Theorem 3.7 was proved by ...

The study of ideal theory in B-algebra was inaugurated by Gelfand [1] to whom

most of the results

**given**in Section 1 are due. B- and B"-algebras. The results ofSection 2 are due to Gelfand [1]. The fundamental Theorem 3.7 was proved by ...

Page 1273

The simplification,

presented in the text. For another proof of the theorem, see Calkin [3] and

Eberlein [2; p. 699], and for applications to partial differential equations, consult

Friedrichs [3].

The simplification,

**given**by Freudenthal [8], of Friedrichs' proof is the onepresented in the text. For another proof of the theorem, see Calkin [3] and

Eberlein [2; p. 699], and for applications to partial differential equations, consult

Friedrichs [3].

Page 1591

The defining property used by them coincides with the property we have

Theorem 4. The development followed in this section and the next, which makes

extensive use of Definition 1, has also been used by Snol [1] and Naimark [5].

The defining property used by them coincides with the property we have

**given**inTheorem 4. The development followed in this section and the next, which makes

extensive use of Definition 1, has also been used by Snol [1] and Naimark [5].

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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additive Akad algebra Amer analytic applied assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complete Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math measure multiplicity neighborhood norm obtained partial positive preceding present problem projection PRoof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero